In this work we continue the study of topological group structure of neutrosophic sets. Some basic properties of neutrosophic topological groups are investigated by giving an alternate de…nition for neutrosophic topological group. It is proved that automorphism of neutrosophic topological groups is neutrosophic homeomorphism.

In this article, we presented eight different types of neutrosophic topological groups, each of which depends on the conceptions of neutrosophic alpha-open sets and neutrosophic alpha-continuous functions. Also, we found the relation between these types, and we gave some properties on the other side.

In this paper we try to introduce neutrosophic bitopological group. We try to investigate some new definition and properties of neutrosophic bitopological group.

The main objective of this study is to introduce the notion of plithogenic neutrosophic hypersoft almost topological group. We have defined some new concepts and investigated properties of regularly open set and regularly closed set and then we observed the definitions of plithogenic neutrosophic hypersoft closed mapping, open mapping and finally we have defined the definition of plithogenic neutrosophic hypersoft almost continuous mapping. By observing the definition of plithogenic neutrosophic hypersoft almost continuous mapping we have studied neutrosophic hypersoft topological group and plithogenic neutrosophic hypersoft almost topological group and some of their properties.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets.

In this chapter, we introduce neutrosophic triplet cosets for neutrosophic triplet G-module and neutrosophic triplet quotient G-module. Then, we give some definitions and examples for neutrosophic triplet quotient G-module and neutrosophic triplet cosets. Also, we obtain isomorphism theorems for neutrosophic triplet G-modules and we prove isomorphism theorems for neutrosophic triplet G-modules.